What is the answer to e^x+e^{-x}=8 ?

The answer to e^x+e^{-x}=8 is x=ln(4+sqrt(15)),x=ln(4-sqrt(15))

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e^x+e^{-x}=8

e^{x} + e^{- x} = 8

x = ln (4 + 15), x = ln (4 - 15)

Decimal Notation

x = 2.06343 \dots, x = - 2.06343 \dots

Solution steps

e^{x} + e^{- x} = 8

Apply exponent rules

e^{x} + (e^{x})^{- 1} = 8

Rewrite the equation with

e^{x} = u

u + (u)^{- 1} = 8

Solve

u + u^{- 1} = 8 : u = 4 + 15, u = 4 - 15

u = 4 + 15, u = 4 - 15

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 4 + 15 : x = ln (4 + 15)

Solve

e^{x} = 4 - 15 : x = ln (4 - 15)

x = ln (4 + 15), x = ln (4 - 15)

2 - 3^{- x} = - 1

3^{x^{2} - x} = 9

2 e^{x} + 3 e^{- 3 x} = 0

2^{x} = 55

2^{x} = - 4

What is the answer to e^x+e^{-x}=8 ?
The answer to e^x+e^{-x}=8 is x=ln(4+sqrt(15)),x=ln(4-sqrt(15))